### Probing local electronic states in the quantum Hall regime with a single-lead quantum dot

**Introduction**

By utilizing a semiconductor quantum dot, we can examine electronic states in solid state devices precisely and locally.

In this experiment, we proved the local electronic states in quantum Hall regime, which are formed in semiconductor devices with magnetic fields.

**Experiment**

The right figures show schematics of our device. A quantum dot is coupled to a Hall bar, in which the quantum Hall states are formed.

We can probe the local electronic states near the dot by measuring the electron tunneling into a dot state.

The right figures show the results of the measurement.

The upper two show the results in quantum Hall regime and the slopes of the black areas depend on terminals. This shows the chirality of the quantum Hall states. The lowest one shows the result in a normal state and there is no chirality.

The right figures show the extracted values of electron temperature from the signal of the electron tunneling.

In normal stats, the temperature increases with the applied voltage bias. In the quantum Hall regimes, no increase of the temperature is observed.

This is the microscopic measurement of suppression of the scattering in the quantum Hall regime.

The right figures show the changes of the local voltage and the electron temperature with the change of magnetic fields.

With the increase of the magnetic field, the quantum Hall states are formed.

In the quantum Hall regimes (gray regions), there is no voltage drop and the electron temperature is kept low reflecting the suppression of the scattering.

The right figures show the details of the electron tunneling signal.

With the increase of the magnetic field, the slope of the line becomes steep. This implies the distance between the dot and the quantum Hall states becomes larger when we decrease the energy of the dot.

This result directly reflects the effect of the charge redistribution in the quantum Hall states.

**Conclusion**

We probed the local electronic states in the quantum Hall regime utilizing a semiconductor quantum dot.

We observed the formation of the quantum Hall states, their chirality, the suppression of the scattering and the charge redistribution in a microscopic way.

**Reference**

“Probing local electronic states in the quantum Hall regime with a side-coupled quantum dot”, Tomohiro Otsuka, Eisuke Abe, Yasuhiro Iye, and Shingo Katsumoto, Physical Review B 81, 245302 (2010).